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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting

Which statement about an effective annual rate of discount d and the effective annual interest rate i (both positive) is correct?

The correct statement is that d = i/(1+i), so d is smaller than i. Discount is measured against the year-end value, which exceeds the opening value, so the same interest gives a smaller rate. The quantity 1/(1+i) is the discount factor v, not d.

  1. Ad is greater than i
  2. Bd = i x (1+i)
  3. Cd = i/(1+i), so d is less than iCorrect
  4. Dd = 1/(1+i)
  5. d equals i only when compounding is continuous

Explanation

Discount is interest divided by the end-of-year amount, so d = i/(1+i), which is always less than i for i > 0. The option d = 1/(1+i) is actually v, the discount factor, not the discount rate.

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